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Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat this for a number of your choice from the second row. You should now have just one number left on the bottom row, circle it. Find the total for the three numbers circled. Compare this total with the number in the centre of the square. What do you find? Can you explain why this happens?

Playing Connect Three

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

In Connect Three, the winner is the first to complete a row of three, either horizontally, vertically or diagonally.

The game is played with two special dice, one with the numbers $1, 2, 3, -4, -5, -6$ and the other with the numbers $-1, -2, -3, 4, 5, 6$.
Choose what order to place the dice in, and add or subtract them to produce one of the totals shown on the board, which you can then cover with one of your counters.

You cannot cover a number which has already been covered.
If you are unable to find a total which has not been covered you must Pass.

The winner is the first to complete a line of three.

Play the game a few times, and then take a look at the questions below.
You can use the interactive version below or print this board to play away from the computer.

Full Screen Version

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Some numbers can only be made in one way, but some can be made in many different ways.
Can you work out the number of different ways of achieving each of the different totals?

Can this help you to develop a strategy to improve your chances of winning?
Can you explain your strategy?